Singularities of diffraction of Cerenkov radiation in a cholesteric liquid crystal

Cerenkov emission in cholesteric liquid crystals is examined theoretically for first-order reflection. The energy lost by a particle per unit frequency per unit azimuth angle as a result of this emission is shown to contain one forbidden band and two polarization-forbidden bands as well as, in general, six square-root singularities on the boundaries of these forbidden bands. It is shown that the radiation intensity on the boundaries of the reflection regions exhibits well-defined beats, and is proportional to the fourth power of the specimen thickness at the intensity maxima. When the particle moves at right-angles to the optical axis of the cholesteric, the differential radiative energy loss is a rapidly-varying function of the position of the particle trajectory